Parts of Circles
Andrew Gloag
Bill Zahner
Dan Greenberg
Jim Sconyers
Lori Jordan
Victor Cifarelli
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Printed: November 21, 2012
AUTHORS
Andrew Gloag
Bill Zahner
Dan Greenberg
Jim Sconyers
Lori Jordan
Victor Cifarelli
EDITOR
Annamaria Farbizio
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C ONCEPT
Concept 1. Parts of Circles
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Parts of Circles
Here you’ll learn all the vocabulary associated with the parts of a circle.
What if you drew a line through a circle from one side to the other that does not pass through the center? What if
you drew a line outside a circle that touched the circle at one point? What would you call these lines you drew?
After completing this Concept, you’ll be able to name circle parts such as these.
Watch This
MEDIA
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Parts ofCirclesCK-12
Watch the first half of this video.
MEDIA
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James Sousa:Introduction toCircles
Guidance
A circle is the set of all points in the plane that are the same distance away from a specific point, called the center.
J
The center of the circle below is point A. We call this circle “circle A,” and it is labeled A.
Important Circle Parts
Radius: The distance from the center of the circle to its outer rim.
Chord: A line segment whose endpoints are on a circle.
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Diameter: A chord that passes through the center of the circle. The length of a diameter is two times the length of
a radius.
Secant: A line that intersects a circle in two points.
Tangent: A line that intersects a circle in exactly one point.
Point of Tangency: The point where a tangent line touches the circle.
−→
The tangent ray T P and tangent segment T P are also called tangents.
Tangent Circles: Two or more circles that intersect at one point.
Concentric Circles: Two or more circles that have the same center, but different radii.
Congruent Circles: Two or more circles with the same radius, but different centers.
Example A
Find the parts of
a) A radius
b) A chord
2
J
A that best fit each description.
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Concept 1. Parts of Circles
c) A tangent line
d) A point of tangency
e) A diameter
f) A secant
Answers:
a) HA or AF
b) CD, HF, or DG
←
→
c) BJ
d) Point H
e) HF
←
→
f) BD
Example B
Draw an example of how two circles can intersect with no, one and two points of intersection. You will make three
separate drawings.
Example C
Determine if any of the following circles are congruent.
From each center, count the units to the outer rim of the circle. It is easiest to count vertically or horizontally. Doing
this, we have:
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From these measurements, we see that
J
Radius of
K
A = 3 units
Radius of
K
B = 4 units
Radius of
K
C = 3 units
A∼
=
J
C.
Notice the circles are congruent. The lengths of the radii are equal.
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Parts ofCirclesCK-12
Guided Practice
1. If the diameter of a circle is 10 inches, how long is the radius?
2. Is it possible to have a line that intersects a circle three times? If so, draw one. If not, explain.
3. Are all circles similar?
Answers:
1. The radius is always half the length of the diameter, so it is 5 inches.
2. It is not possible. By definition, all lines are straight. The maximum number of times a line can intersect a circle
is twice.
3. Yes. All circles are the same shape, but not necessarily the same size, so they are similar.
Practice
Determine which term best describes each of the following parts of
1. KG
4
J
P.
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2.
3.
4.
5.
6.
7.
8.
9.
Concept 1. Parts of Circles
←
→
FH
KH
E
←
→
BK
←
→
CF
A
JG
What is the longest chord in any circle?
Use the graph below to answer the following questions.
10.
11.
12.
13.
14.
Find the radius of each circle.
Are any circles congruent? How do you know?
J
J
Find all the common tangents for B and C.
J
J
C and E are externally tangent. What is CE?
Find the equation of CE.
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